Derive orthogonal (and chirality) for products of orthogonal tensors

[petlenz]

Summary

The product of orthogonal tensors is orthogonal: Q₁·Q₂ is orthogonal when both Q₁, Q₂ are. The CAS drops the annotation. Chirality composes too (relevant to #269): proper·proper → proper, proper·improper → improper, improper·improper → proper.

Math

(Q₁Q₂)ᵀ(Q₁Q₂) = Q₂ᵀ Q₁ᵀ Q₁ Q₂ = Q₂ᵀ Q₂ = I → orthogonal. det(Q₁Q₂) = det(Q₁)det(Q₂), so the ±1 determinant (proper/improper) multiplies.

Current behavior (probed)

Q*Q2   (both orthogonal)   -> (none)   expected: orth

How to fix

Two parts:

1. Binary hook in tag_invoke(mul_fn, tensor, tensor) (include/numsim_cas/tensor/tensor_operators.h): after building the product, if (is_orthogonal(lhs) && is_orthogonal(rhs)) result.data()->tensor_algebra_assumptions().insert(orthogonal{});. Beware the existing trans(Q)·Q → I fold fires first for the transpose pair — that path returns identity and is unaffected.

2. Chirality composition (optional, ties into Add chirality sub-tag to refine det(orthogonal) fold (proper vs improper rotation) #269): if both are proper_rotation → insert proper_rotation; mixed → improper_rotation; both improper → proper_rotation. Only when both factors carry a chirality tag; otherwise fall back to plain orthogonal.

3. N-ary generalization: an all-orthogonal tensor_mul factor list → orthogonal. Fold into the classify_tensor_mul_space classifier used by the sandwich issues so multi-factor Q₁Q₂Q₃… is covered.

How to test

auto Q1 = mk("Q1", 3); assume_orthogonal(Q1);
auto Q2 = mk("Q2", 3); assume_orthogonal(Q2);
EXPECT_TRUE(is_orthogonal(Q1 * Q2));
// chirality (if implemented, uses assume_proper_rotation / assume_improper_rotation from #269):
auto R1 = mk("R1", 3); assume_proper_rotation(R1);
auto R2 = mk("R2", 3); assume_improper_rotation(R2);
EXPECT_TRUE(is_improper_rotation(R1 * R2));   // det = (+1)(-1) = -1
// safety: mixing orthogonal with a general tensor drops it
EXPECT_FALSE(is_orthogonal(Q1 * mk("G",3)));

Part of the annotation-completeness umbrella below. Chirality piece relates to #269.

[petlenz]

Tracked under the annotation-completeness umbrella #396 (full gap table + tiered rollout plan there).